This paper proposes a novel methodology for robust analog/mixed-signal IC design by introducing a notion of budget of uncertainty. This method employs a new conic uncertainty model to capture process variability and describes variability-affected circuit design as a set-based robust optimization problem. For a pre-specified yield requirement, the proposed method conducts uncertainty budgeting by associating performance yield with the size of uncertainty set for process variations. Hence the uncertainty budgeting problem can be further translated into a tractable robust optimization problem. Compared with the existing robust design flow based on ellipsoid model, this method is able to produce more reliable design solutions by allowing varying size of conic uncertainty set at different design points. In addition, the proposed method addresses the limitation that the size of ellipsoid model is calculated solely relying on the distribution of process parameters, while neglecting the dependence of circuit performance upon these design parameters. The proposed robust design framework has been verified on various analog/mixed-signal circuits to demonstrate its efficiency against ellipsoid model. An up to 24% reduction of design cost has been achieved by using the uncertainty budgeting based method.